1. The Height Equation

2. h= ending height g = gravity constant (32 if feet, 9.8 if meters) v 0 = initial velocity h 0 = initial height t = time

3. Example 1 Find the maximum height of an object shot upward from the earth’s surface with an initial velocity of 106 ft/sec

4. Solution Step 1 – Write the equation h = -16t 2 + 106t + 0 Step 2 – put it in your calculator, go to y =, put it in changing t’s to x’s. y = -16x 2 +106x Step 3 – Graph by pushing zoom fit (zoom 0) zoom in or out until you get a good picture of the parabola Step 4 – Find the maximum. This is an ordered pair. The x is time and the y is height – this is always true!! Your solution is the x coordinate of the max. 175.56 seconds

5. Example 2 A ball is thrown vertically upward at an initial speed of 48 ft/sec from the top of a building 2000 feet high. How high does the ball go?

6. Solution Step 1 – h = -16t 2 + 48t + 2000 Step 2 – graph it!! Step 3 – Find the max Step 4 – the answer is the y- coordinate of the max. 2036 feet

7. Example 3 A ball is thrown straight up with an initial velocity of 56 ft/sec. The height of the ball in seconds after it is thrown is given by what equation? What is the maximum height of the ball? What is the height of the ball after 1 second? After how many seconds will the ball return to the ground?

8. Solution Equation: h=-16t 2 + 56t Max Height: 49 feet Height after 1 sec: 40 feet Explanation: to find the max height you should go to 2 nd trace, value, then x = 1 Time it takes to hit the ground: 3.5 sec Explanation: to find when an object hits the ground you are looking for the x-intercept (or zero) on the right hand side of your graph. You can find this by using the following steps: »1. Go back to y= and put 0 in the y 2 equation. »2. Hit graph »3. Go to 2 nd trace, intersection (5), move your cursor over to the right hand x – intercept, then hit enter 3 times. You are looking for the x value.

9. Example 4 A ball is dropped from the top of a 500 ft building with an initial velocity of 32ft/sec. How long does it take the ball to reach the ground? Answer: 6.68 seconds Explanation: Graph and find the right hand x - intercept. Need directions: go back to the last slide and follow the steps for “time it takes to hit the ground”.

10. Example 5 A ball is thrown from the top of a tower at a velocity of 10 m/sec. The ball hit the ground at the base of the tower 4 seconds later. How high is the tower? Answer: 38.4 meters Explanation: